Solve for $x$ and $y$ using elimination. ${-2x+4y = 12}$ ${2x-5y = -16}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-2x+4y = 12}\thinspace$ to find $x$ ${-2x + 4}{(4)}{= 12}$ $-2x+16 = 12$ $-2x+16{-16} = 12{-16}$ $-2x = -4$ $\dfrac{-2x}{{-2}} = \dfrac{-4}{{-2}}$ ${x = 2}$ You can also plug ${y = 4}$ into $\thinspace {2x-5y = -16}\thinspace$ and get the same answer for $x$ : ${2x - 5}{(4)}{= -16}$ ${x = 2}$